Saving behaviour and health: A high-dimensional Bayesian analysis of British panel data

Figures & data

Figure 1. Distribution of the amount saved.

Figure 2. Distribution of the amount saved where saving is greater than zero.

Figure 3. Distribution of financial assets.

Figure 4. Distribution of financial assets where financial assets are greater than zero.

Table 1. Summary Statistics: Dependent Variables

Variable	Mean	(Std. Dev.)
Save (Binary)	45.85%
Ln(Amount Saved) (All Individuals)	2.269	(2.591)
Amount Saved (All Individuals)	119.605	(275.314)
Ln(Amount Saved) (Individuals who save)	4.948	(1.173)
Amount saved (Individuals who save)	260.84	(358.465)
Financial Investments (Binary)	61.90%
Ln(Financial Investments) (All individuals)	4.911	(4.349)
Financial Assets	11,798.75	(37,490.32)
Ln(Financial Investments) (Individuals who hold financial assets)	7.934	(2.562)
Financial Assets (Individuals who hold financial assets)	19,060.40	(46,179.05)
Unsecured Debt (Binary)	39.2%
Ln(Unsecured Debt) (All individuals)	3.109	(4.003)
Unsecured debt (All individuals)	2,770.385	(7,360.036)
Ln(Unsecured Debt) (Individuals who hold unsecured debt)	7.926	(1.630)
Unsecured debt (Individuals who hold unsecured debt)	7062.382	(10383.72)
N	3,365

Notes: Saving is based on the questions: “Do you save any amount of your income, for example, by putting something away now and then in a bank, building society, or Post Office account other than to meet regular bills? About how much, on average, do you manage to save a month?” Financial investments are based on the questions: “I'd like to ask about any savings or investments you may have. Which of these savings accounts do you have, if any? Savings or deposit accounts, National Savings Accounts, ISA - cash only, ISA - stocks and shares, or PEPs, Premium Bonds or Other types of savings accounts”; and “What is the amount held in each of these accounts”. Debt holding is based on the question: “I would now like to ask you about any other financial commitments you may have apart from mortgages. For which, if any, of these items do you currently owe any money? Please do not include credit card and other bills being fully paid off in the current month”; and “About how much in total is owed?” If an individual responds “yes” to the first question, the binary variable is equal to one, zero otherwise. The amount of the variable is then captured by the second question.

Table 2. Summary statistics: health measures.

Health measure	Mean	Standard deviation
Composite Biomarkers
Allostatic Load – Clinical Cut	3.117	(2.019)
Allostatic Load – Z-Score	−0.343	(6.907)
Individual Biomarkers
General Health
Ln(CHL/HDL)	1.282	(0.344)
CHL/HDL	3.832	(1.433)
Ln(HbA1c)	3.557	(0.154)
HbA1c	35.538	(7.065)
Ln(BMI)	3.311	(0.185)
BMI	27.919	(5.786)
Inflammatory Markers
Ln(CRP)	0.236	(0.941)
CRP	1.950	(1.927)
Liver Function
Ln(ALB)	3.856	(0.057)
ALB	47.376	(2.678)
Self-Assessed Health Measures
SF-12	0.788	(0.134)
SAH	2.564	(1.062)
N	3,365

Notes: Ln(.) denotes natural logarithm. Allostatic load – clinical cut is defined as the sum of the binary variables indicating whether individuals have non-normal levels based on clinical guidance of cut-off points whilst the Z-score measure of allostatic load is a continuous explanatory variable, where an individual's Z-score represents the absolute value of the standardised distance between their level of a given biomarker and the population mean for that biomarker and summed across all biomarkers. CHL/HDL is the ratio of total cholesterol to high density cholesterol. HbA1c is a measure of glycated haemoglobin; an indicator of diabetes risk and is measured in mmol/mol. CRP, c-reactive protein is an inflammatory marker measured in mg/L. Alb is indicative for Albumin, and is measured in g/L. BMI is defined as kg/m². SF-12 is the preference based continuous index derived from the Short Form 12 questionnaire, whilst self-assessed health (SAH) is based on the question: ‘Overall how is your health?’, measured on a five-point scale ranging from ‘excellent’ to ‘very poor’.

Figure 5. Allostatic load index: clinical cut-offs.

Figure 6. Allostatic load ndex: z-scores.

Table 3. Summary statistics: independent variables.

Variables	Mean	Standard Deviation
Age	44.74	(10.48)
Age Squared	2111.78	(911.54)
Female*	56.7
Education (Omitted Category: Below GCSE)
Degree*	29.5
Other Higher Qualification*	14.6
A-Level*	21.1
GCSE*	21.4
Other Qualification*	7.49
Relationship Status (Omitted Category: Single/never married)
Married*	72.60
Divorced*	11.4
Widow*	1.43
Number of Children	0.73	(0.99)
Employment status (Omitted Category: Unemployed/Not in the labour force)
Employed*	70.60
Self-Employed*	9.72
Retired*	3.15
Ln(Household Monthly Income)	8.18	(0.67)
Household Monthly Income	4364.10	(2831.39)
Region (Omitted Category: Residing in London)
North East*	6.45
North West*	11.53
Yorkshire*	9.21
East Midlands*	10.37
West Midlands*	9.26
East*	10.22
South East*	15.96
South West*	11.68
Wales*	2.64
Scotland*	4.93
Arrears*	13.88
Material Deprivation	1.420	(2.02)
N	3,365

Note: Mean and standard deviation are reported for continuous variables and proportions are reported for binary independent variables. *denote binary variables.

Table 4. A semi-continuous model of monthly saving.

	Binary Part			Continuous Part
Independent Variables	Mean	2.50%	97.50%	Mean	2.50%	97.50%	Marginal Effects†
Age	−0.528	−1.206	0.148	−0.004	−0.048	0.039	−0.461
Age Squared	0.342	−0.350	1.029	0.000	0.000	0.001	0.296
Female	0.060	−0.098	0.219	−0.256*	−0.364	−0.148	−0.205
Degree	0.284	−0.126	0.704	0.612*	0.290	0.938	0.832
Other Higher Qualification	0.296	−0.126	0.730	0.450*	0.117	0.791	0.678
A-Level	0.243	−0.163	0.671	0.368*	0.046	0.703	0.560
GCSE	0.053	−0.358	0.481	0.105	−0.226	0.440	0.150
Other Qualification	0.065	−0.419	0.543	0.013	−0.362	0.392	0.068
Married	−0.379*	−0.650	−0.105	−0.060	−0.242	0.124	−0.437
Divorced	−0.045	−0.389	0.308	−0.086	−0.335	0.159	−0.126
Widow	0.313	−0.380	1.040	−0.009	−0.488	0.465	0.231
White	0.116	−0.239	0.467	0.063	−0.192	0.319	0.159
Number of Children	−0.073	−0.167	0.019	−0.140*	−0.206	−0.075	−0.203
Employed	0.731*	0.470	1.000	0.438*	0.232	0.647	0.910
Self-Employed	0.345*	0.004	0.688	0.576*	0.313	0.841	0.837
Retired	0.256	−0.250	0.770	0.150	−0.254	0.544	0.351
Ln(Household Monthly Income)	0.234*	0.135	0.335	0.569*	0.465	0.675	0.772
North East	0.062	−0.362	0.490	−0.134	−0.430	0.155	−0.082
North West	0.220	−0.152	0.592	−0.295*	−0.543	−0.043	−0.120
Yorkshire	0.108	−0.277	0.486	−0.029	−0.300	0.243	0.061
East Midlands	0.199	−0.177	0.573	−0.041	−0.296	0.222	0.119
West Midlands	0.166	−0.222	0.545	−0.046	−0.301	0.209	0.089
East	0.175	−0.206	0.546	−0.154	−0.411	0.105	−0.012
South East	0.159	−0.185	0.499	−0.060	−0.297	0.177	0.070
South West	0.130	−0.239	0.502	−0.092	−0.346	0.167	0.015
Wales	−0.263	−0.839	0.301	−0.134	−0.553	0.285	−0.385
Scotland	0.190	−0.257	0.637	−0.282	−0.587	0.028	−0.129
Arrear	−0.069	−0.345	0.201				−0.208
Material Deprivation	−0.493*	−0.553	−0.432				−0.446
N	3,365

Notes: *denotes statistically significant at the 5% level. Mean indicates the estimated coefficient, whilst 2.50% and 97.50% denote the 95% credible interval.

†Marginal effects are calculated in the following way:

Continuous independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\beta .\frac{\phi ({\mathrm{\Phi }}^{-1}(\pi ))}{\pi }+\gamma$;

Binary independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\text{ln}\left(\frac{\mathrm{\Phi }(\beta +{\mathrm{\Phi }}^{-1}(\pi ))}{\pi }\right)+\gamma$.

Where $\phi$ and $\mathrm{\Phi }$ are the p.d.f and the c.d.f of the standard normal distribution, respectively, $\beta$ is the coefficient in the binary part of the model, $\gamma$ is the coefficient in the continuous part, whilst π is the probability that saving is positive. In this case we take π to equal the sample proportion, that is, 0.4585.

Table 5. Summary of health measures in the semi-continuous model of monthly saving.

	Binary Part			Continuous Part
Health Measures	Mean	2.50%	97.50%	Mean	2.50%	97.50%	Marginal Effects†
Self-Assessed Health
SAH^¶	0.117*	0.037	0.198	0.149*	0.091	0.208	0.154
SF-12	0.732*	0.098	1.361	0.570*	0.123	1.012	1.204
Biomarkers
Composite Biomarkers
Allostatic Load – Clinical Cut	−0.276*	−0.420	−0.133	−0.100	−0.200	0.001	−0.339
Allostatic Load – Z-Score	−0.528*	−0.798	−0.251	−0.204*	−0.393	−0.014	−0.661
Individual Biomarkers
General Health
Ln(CHL/HDL)	−0.436*	−0.655	−0.212	−0.133	−0.285	0.019	−0.511
Ln(HbA1c)	−0.612*	−0.933	−0.279	−0.249*	−0.479	−0.017	−0.779
Ln(BMI)	−0.278*	−0.432	−0.128	−0.093*	−0.195	0.009	−0.334
Inflammatory markers
Ln(CRP)	−0.204*	−0.324	−0.085	−0.089*	−0.168	−0.007	−0.266
Liver Function
Ln(ALB)	0.743*	0.205	1.273	0.713*	0.346	1.076	1.357
N	3,365

Notes: All health measures are included independently along with the independent variables included in Table 4 and outlined in Section 3.3. The results relating to the control variables are qualitatively the same as those presented in Table 4, that is, they generally display the same sign and significance level.

*denotes statistically significant at the 5% level. Mean indicates the estimated coefficient, whilst 2.50% and 97.50% denote the 95% credible interval.

†Marginal effects are calculated in the following way: Continuous independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\beta \frac{\phi ({\mathrm{\Phi }}^{-1}(\pi ))}{\pi }+\gamma$; and binary independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\text{ln}\left(\frac{\mathrm{\Phi }(\beta +{\mathrm{\Phi }}^{-1}(\pi ))}{\pi }\right)+\gamma$. Where $\phi$ and $\mathrm{\Phi }$ are the p.d.f and the c.d.f of the standard normal distribution, respectively, $\beta$ is the coefficient in the binary part of the model, $\gamma$ is the coefficient in the continuous part, whilst π is the probability that saving is positive. In this case, we take π to equal the sample proportion, that is, 0.4585.

^¶ Marginal effect presented is for the change from 0 to 1, corresponding to a change from poor to fair health. The marginal effect is calculated in the following way: $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\frac{1}{(b-a)}\text{ln}\left(\frac{\mathrm{\Phi }(\beta b+{\mathrm{\Phi }}^{-1}(\pi ))}{\mathrm{\Phi }(\beta a+{\mathrm{\Phi }}^{-1}(\pi ))}\right)+\gamma$. The marginal effects relating to changes from fair to good health, good to very good health, and very good to excellent health are 0.141, 0.127 and 0.113, respectively.

Table 6. Summary of health measures in semi-continuous model of financial assets.

	Binary Part			Continuous Part
Health Measures	Mean	2.50%	97.50%	Mean	2.50%	97.50%	Marginal effects^†
Self-Assessed Health
SAH^¶	0.139*	0.057	0.222	0.359*	0.255	0.465	0.307
SF-12	0.238	−0.397	0.860	1.725*	0.902	2.539	1.872
Biomarkers
Composite Biomarkers
Allostatic Load – Clinical Cut	−0.235*	−0.385	−0.083	−0.366*	−0.555	−0.175	−0.511
Allostatic Load – Z-Score	−0.432*	−0.724	−0.144	−0.735*	−1.093	−0.377	−1.001
Individual Biomarkers
General Health
Ln(CHL/HDL)	−0.352*	−0.588	−0.114	−0.537*	−0.829	−0.250	−0.754
Ln(HbA1c)	−0.551*	−0.891	−0.210	−0.919*	−1.349	−0.486	−1.258
Ln(BMI)	−0.228*	−0.387	−0.068	−0.382*	−0.579	−0.187	−0.522
Inflammatory markers
Ln(CRP)	−0.179*	−0.302	−0.054	−0.300*	−0.450	−0.146	−0.410
Liver Function
Ln(ALB)	0.837*	0.305	1.380	1.948*	−2.439	−0.052	−0.734
N	3,365

Notes: All health measures are included independently along with the independent variables included in Table 4 and outlined in Section 3.3. The results relating to the control variables are qualitatively the same as those presented in Table 4, that is, they generally display the same sign and significance level.

*denotes statistically significant at the 5% level. Mean indicates the estimated coefficient, whilst 2.50% and 97.50% denote the 95% credible interval.

† Marginal effects are calculated in the following way: Continuous independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\beta \frac{\phi ({\mathrm{\Phi }}^{-1}(\pi ))}{\pi }+\gamma$; and binary independent variables $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\text{ln}\left(\frac{\mathrm{\Phi }(\beta +{\mathrm{\Phi }}^{-1}(\pi ))}{\pi }\right)+\gamma$. Where $\phi$ and $\mathrm{\Phi }$ are the p.d.f and the c.d.f of the standard normal distribution, respectively, $\beta$ is the coefficient in the binary part of the model, $\gamma$ is the coefficient in the continuous part, whilst π is the probability that saving is positive. In this case, we take π to equal the sample proportion, that is, 0.6190.

^¶ Marginal effect presented is for the change from 0 to 1, corresponding to a change from poor to fair health. The marginal effect is calculated in the following way: $\frac{\mathrm{\Delta }E(y|x)}{E(y|x)}=\frac{1}{(b-a)}\text{ln}\left(\frac{\mathrm{\Phi }(\beta b+{\mathrm{\Phi }}^{-1}(\pi ))}{\mathrm{\Phi }(\beta a+{\mathrm{\Phi }}^{-1}(\pi ))}\right)+\gamma$. The marginal effects relating to changes from fair to good health, good to very good health, and very good to excellent health are 0.288, 0.269 and 0.249, respectively.

Table 7. Joint semi-continuous model of financial assets and unsecured debt holding.

	Financial Assets						Total Unsecured Debt
	Binary Part			Continuous Part			Binary Part			Continuous Part
Health Measures	Mean	2.5%	97.5%	Mean	2.5%	97.5%	Mean	2.5%	97.5%	Mean	2.5%	97.5%
Composite Biomarkers
Allostatic Load – Clinical Cut	−0.144*	−0.233	−0.052	−0.375*	−0.558	−0.181	0.018	−0.065	0.105	−0.030	−0.190	0.134
Allostatic Load – Z-Score	−0.258*	−0.423	−0.086	−0.771*	−1.122	−0.407	0.067	−0.090	0.222	−0.002	−0.294	0.311
Individual Biomarkers
General Health
Ln(CHL/HDL)	−0.218*	−0.361	−0.091	−0.593*	−0.875	−0.31	0.029	−0.101	0.153	0.038	−0.211	0.270
Ln(HbA1c)	−0.238*	−0.376	−0.106	−0.796*	−1.111	−0.498	−0.009	−0.132	0.115	0.183	−0.059	0.439
Ln(BMI)	−0.120*	−0.215	−0.024	−0.357*	−0.561	−0.153	0.064	−0.022	0.151	−0.014	−0.184	0.153
Inflammatory markers
Ln(CRP)	−0.110*	−0.180	−0.037	−0.321*	−0.476	−0.164	0.028	−0.044	0.096	−0.001	−0.130	0.128
Liver Function
Ln(ALB)	0.259*	0.097	0.421	1.076*	0.714	1.433	0.012	−0.148	0.162	−0.245	−0.568	0.042
Self-Assessed Health
SAH	0.089*	0.035	0.139	0.387*	0.278	0.499	−0.050	−0.101	0.001	0.095*	0.003	0.183
SF-12	0.018	−0.031	0.068	0.242*	0.136	0.359	−0.052*	−0.100	−0.007	0.077	−0.012	0.164
N	3,365

Notes: All health measures are included independently along with the independent variables included in Table 4 and outlined in Section 3.3. The results relating to the control variables are qualitatively the same as those presented in Table 4, that is, they generally display the same sign and significance level.

*denotes statistically significant at the 5% level. Mean indicates the estimated coefficient, whilst 2.50% and 97.50% denote the 95% credible interval.